A characterization of the bidisc by a subgroup of its automorphism group

We make a connection between the structure of bidisc and distinguished subgroup its automorphism group. The group bidisc, as we know, is dimension six acts transitively. observe that it contains isomorphic to open unit disc this partitions into complex curve family strongly pseudo-convex hypersurfaces are non-spherical CR-manifolds. Our work reverses process shows any 2-dimensional Kobayashi-hyperbolic manifold whose (which known, from general theory, be Lie group) has 3-dimensional non-solvable (as on produce collection orbits possessing essentially characteristics concretely known mentioned above, biholomorphic bidisc. interesting in own right. It turns out if consider subdomain union proper sub-collection then can expressed very simply terms subgroup.